Geometry Regents Review

When partitioning a line segment into a 1:4 ratio, how many total 'parts' are there?

5

To map a regular polygon onto itself, use this formula

360 / number of sides (don't forget multiples of that answer work too)

slopes of parallel lines are

equal

slopes of perpendicular lines are

negative reciprocals

rotating a triangle continuously will always form a

cone

rotating a rectangle continuously will always form a

cylinder (like a revolving door)

If a cut is made parallel to a solid's base, the cross section is

the same shape as the base

If a cut is made perpendicular to a solid's base, the cross section is

the same shape as the sides

When dilating a line, if the center is on the line...

keep the equation the same

When dilating a line, if the center is off the line...

keep the slope, multiply the y-intercept by the scale factor

sinA=

cosB

If sin(2x+5)=cos(3x-5), what should you do?

2x+5+3x-5=90

When finding area of a non-right triangle (and it's not a graph paper question), use this formula

A=1/2absinC (a&b are sides, C is an angle)

The exterior angle of a triangle is equal to...

the sum of the nonadjacent interior angles

A median goes from a vertex (corner) to a _____

midpoint

Altitude is a synonym for this

height

For cylinders & cones, change B in V=Bh to this

πr²

Density =

mass/volume

Population Density =

population density/area

Name the 5 methods for proving triangles are congruent.

SAS, SSS, ASA, AAS, HL

Name the 3 methods for proving triangles are similar.

AA, SAS, SSS (all written proofs are AA)

To determine if 3 sides form a triangle,

the sum of the smaller two sides must be greater than the third side

A pentagon has ____ sides

5

A hexagon has ____ sides

6

An octagon has ____ sides

8

A decagon has ____ sides

10

sinθ=

opposite/hypotenuse

cosθ=

adjacent/hypotenuse

tanθ=

opposite/adjacent

If the circle equation is (x+3)²+(y-4)²=16, what is the center and radius?

center (-3,4), r=4

A parallelogram must be a rhombus if _______. (2 correct answers)

*the diagonals are perpendicular

*all sides are congruent

A parallelogram must be a rectangle if _________. (2 correct answers)

*the diagonals are congruent

*consecutive sides are perpendicular

rule for reflection over y=x

(x,y)→(y,x)

rule for rotation of 180° about the origin (also works for point reflection)

(x,y)→(-y,-x)

rule for rotation of 90° CCW about the origin

(x,y)→(-y,x)

rule for rotation of 270° CCW about the origin

(x,y)→(y,-x)

a triangle has ____ degrees

180

a quadrilateral has ____ degrees

360

Name the 6 steps of a proof.

G - write the givens

E - explain the givens

R - reflexive property

V - vertical angles

T - prove triangles congruent or similar

C - CPCTC or CSSSTP

Area of a rectangle formula

A=lw

Area of a triangle formula

A=½bh

Area of sector formula

(central angle/360) πr²

Arc length formula

(central angle/360) 2πr

A central angle is _____ to its intercepted arc

equal

An inscribed angle is ____ of its intercepted arc

half

Coordinate proof: What to do if it asks prove ABC is a right triangle

find distance of 3 sides and make sure they work with Pythagorean Theorem (or use slope to show 2 sides are perpendicular)

Coordinate proof: What to do if it asks prove ABCD is a parallelogram

Distance formula 4x to show opposite sides congruent

Coordinate proof: What to do if it asks prove ABCD is a rectangle

Distance formula 6x to show opposite sides congruent and diagonals congruent

Coordinate proof: What to do if it asks prove ABCD is a rhombus

Distance formula 4x to show all sides congruent

Coordinate proof: What to do if it asks prove ABCD is a square

Distance formula 6x to show all sides congruent and diagonals congruent

Coordinate proof: What to do if it asks prove ABCD is a trapezoid

Slope formula 2x to show one pair of opposite sides are parallel

Coordinate proof: What to do if it asks prove ABCD is an isosceles trapezoid

Slope formula 2x and distance formula 2x

point-slope form

y-y₁=m(x-x₁)

distance formula

√(x₂-x₁)²+(y₂-y₁)²

midpoint formula

(average of x's, average of y's)

Name the 3 rigid motions.

translation, reflection, rotation

Name a transformation that is NOT a rigid motion.

dilation

In an inscribed quadrilateral, the opposite angles are ________.

supplementary (add to 180)

In similar figures, corresponding sides are ____________.

proportional

In similar figures, corresponding angles are ______________.

congruent

If a shape expands left and right, but not up and down, this is called a __________________.

horizontal stretch

If a shape expands up and down, but not left and right, this is called a __________________.

vertical stretch

Circle formula when given 2 secants and finding a missing length

outside x whole = outside x whole

Circle formula when given a tangent and secant and finding a missing length

outside x whole = tangent²

circle formula when given intersecting chords and finding a missing length

segment x segment = segment x segment

circle formula when finding an angle IN the circle

add the arcs and divide by 2

circle formula when finding an angle OUTSIDE the circle

subtract the arcs and divide by 2

An isosceles triangle has _____ equal sides.

2

The ______ angles of an isosceles triangle are congruent.

base

A midsegment of a triangle is ________ the length of the parallel side.

half

To find perimeter when given coordinates....

Find the length of the sides using distance formula and add them up

To find area when given a shape on graph paper...

use the box it in method

The 2 acronyms used when a big right triangle is split into 2 smaller right triangles

HLLS & SAAS

When should you round on a problem?

only on the last step

When to use pencil on the Regents

graphs & constructions